SUMMARY

Trap-jaw ants of the genus Odontomachus produce remarkably fast
predatory strikes. The closing mandibles of Odontomachus bauri, for
example, can reach speeds of over 60 m s–1. They use these
jaw strikes for both prey capture and locomotion – by striking hard
surfaces, they can launch themselves into the air. We tested the hypothesis
that morphological variation across the genus is correlated with differences
in jaw speeds and accelerations. We video-recorded jaw-strikes at 70
000–100 000 frames s–1 to measure these parameters and
to model force production. Differences in mean speeds ranged from
35.9±7.7 m s–1 for O. chelifer, to
48.8±8.9 m s–1 for O. clarus desertorum.
Differences in species' accelerations and jaw sizes resulted in maximum strike
forces in the largest ants (O. chelifer) that were four times those
generated by the smallest ants (O. ruginodis). To evaluate
phylogenetic effects and make statistically valid comparisons, we developed a
phylogeny of all sampled Odontomachus species and seven outgroup
species (19 species total) using four genetic loci. Jaw acceleration and
jaw-scaling factors showed significant phylogenetic non-independence, whereas
jaw speed and force did not. Independent contrast (IC) values were used to
calculate scaling relationships for jaw length, jaw mass and body mass, which
did not deviate significantly from isometry. IC regression of angular
acceleration and body size show an inverse relationship, but combined with the
isometric increase in jaw length and mass results in greater maximum strike
forces for the largest Odontomachus species. Relatively small
differences (3%) between IC and species-mean based models suggest that any
deviation from isometry in species' force production may be the result of
recent selective evolution, rather than deep phylogenetic signal.

INTRODUCTION

Arthropods are renowned for their morphological variation, and many species
have evolved extreme mechanical abilities for a variety of functions such as
the remarkable jumping ability of fleas, and the crushing strikes of
stomatopods (Bennet-Clark and Lucey,
1967; Patek et al.,
2004). These extreme speeds and accelerations are often achieved
with the help of specific innovations such as latches, lever arms, and spring
mechanisms that help store and release high amounts of energy
(Gronenberg, 1996a). It has
been argued that these abilities are optimized in such a way that tradeoffs
between mechanical abilities (benefits) and physiological requirements for
maintaining them (costs) are balanced against the greatest required
performance for that feature (Weibel and
Taylor, 1998). But in nature, where animals evolve in response to
a variety of selective pressures in a changing environment, optimal
performance in any one context may be constrained by physical laws,
developmental programs and phylogenetic history. This is particularly true if
an adaptive feature or mechanism has multiple functions – optimizing it
for one function may result in sub-optimal performance in another, or
competing demands may leave performance in an intermediate range for a
plurality of functions.

The jaw strikes of trap-jaw ants were characterized morphologically and
neurobiologically in a series of papers by Gronenberg and colleagues
(Gronenberg, 1995a;
Gronenberg, 1995b;
Gronenberg, 1996b;
Gronenberg and Tautz, 1994;
Just and Gronenberg, 1999) and
jaw strikes of the species Odontomachus bauri Emery 1982 can reach
extremely high speeds, of over 60 m s–1
(Patek et al., 2006). Beyond
providing the ants with the ability to disable prey, the jaw snaps have been
evolutionarily co-opted for ballistic locomotion. It has long been known that
trap-jaw ants jump (Wheeler,
1922), but only recently has the way they use their jaws to do so
been characterized. These movements take the forms of `bouncer defense' jumps
(Carlin and Gladstein, 1989),
where the ants are propelled horizontally away from a threat, and `escape
jumps', where the jaws are placed against or aimed at the substrate then
fired, launching the ant into the air upon triggering
(Patek et al., 2006). However,
O. bauri is just one of approximately 60 species in the genus
Odontomachus, and while all members of the genus share the same
general trap-jaw morphology, there are morphological and ecological
differences between species that provide the basis for comparative study.

Across the pantropically distributed genus Odontomachus, species
vary considerably in their ecology (Deyrup
and Cover, 2004), including nest site substrates and types of
prey, as well as varying morphologically, covering a range of body sizes and
mandible lengths. These differences suggest that there may be variation in the
performance of the strikes among species (perhaps based on speed or chemical
defenses of common prey, or the relative advantage of jumping ability in nests
or foraging areas with different physical characteristics) and may provide
insight into the co-option of the mandibles for locomotion as well as prey
capture. Thus multi-species comparisons are informative for characterizing
trap-jaw morphology and performance and, more generally, for understanding how
a multi-functional system may be optimized, or constrained, relative to its
various functions.

The goals of this study were to: (1) collect kinematic and morphometric
data for eight species of the trap-jaw ant genus Odontomachus; (2)
construct a phylogenetic hypothesis for these species; and (3) generate a
model for force production based on phylogenetically corrected body size
scaling equations, and compare this modeled range to the observed range across
the eight species measured in this study.

MATERIALS AND METHODS

Phylogeny

In order to detect phylogenetic effects in our comparative data, and to
correct for the problems of non-independence that can invalidate statistical
comparisons between species (Felsenstein,
1985), we developed a phylogenetic hypothesis for a sampling of
species, including the eight species for which we collected strike data. We
generated sequence data for 19 species including 12 Odontomachus and
seven outgroup taxa from other ponerine genera. Portions of four genes were
used: the mitochondrial gene for cytochrome oxidase 1 (COI), the
large subunit (28S) ribosomal RNA gene, and the nuclear
protein-encoding genes wingless (wg) and long-wavelength
rhodopsin (LWR). Primer information is provided in
Table 1. A variable-length
intron in the sequenced section of rhodopsin proved difficult to
align among the outgroup taxa and was included only for the Anochetus
and Odontomachus species. After excluding 29 bp of ambiguously
aligned 28S data we were left with 2685 bp of aligned, concatenated
sequence data. Taxon information and GenBank accession numbers are given in
Table 2. Final deposition of
molecular voucher specimens used in this study (currently held in personal
collection of C.A.S.) will be in the United States Museum of Natural History
(Smithsonian).

Genomic DNA was extracted from one or two legs of a single adult specimen
for each taxon, using the DNEasy Tissue Kit (Qiagen Inc., Valencia,
California, USA). PCR amplification generally consisted of 40 cycles of 20 s
at 94°C, 20 s at 48°–54°C (typically 48°C for 28S and
50–54°C for the other genes), and 50 s at 65°C, with an initial
denaturation of 2 min at 94°C and a final extension of 3 min at 65°C.
For most amplifications a total reaction volume of 20 μl was used,
including 1 unit of HotMaster Taq (Eppendorf AG, Hamburg, Germany), 0.16 mmol
l–1 dNTP mix (Eppendorf AG, Hamburg Germany), 0.5 μmol
l–1 each primer, and 1 or 2 μl of DNA template. PCR
products were cleaned and sequenced by the GATC core sequencing facility on
the University of Arizona campus. Sequences were aligned manually in MacClade
4.08 (Maddison and Maddison,
2005).

Phylogenetic analysis was conducted using a partitioned Bayesian approach
in MrBayes 3.1.2 (Huelsenbeck and
Ronquist, 2001). Protein-coding genes were partitioned by gene and
codon position, with one partition for 28S and an additional
partition for the rhodopsin intron (giving 11 total partitions). An
exploratory MrBayes analysis was performed in which each partition was given a
GTR+I+G model (nst=6, rates=invgamma) and all parameters were unlinked across
partitions. Examination of the resulting parameter sampling in Tracer 1.3
(Rambaut and Drummond, 2004)
suggested the adequacy of a reduced model: GTR+I (nst=6, rates=propinv) for
first and second codon positions and for 28S, HKY+I (nst=2, rates=propinv) for
third codon positions of wingless and rhodopsin and for the
rhodopsin intron, and HKY+I+G (nst=2, rates=invgamma) for third codon
positions of cytochrome oxidase 1. A final analysis was performed
using this modeling scheme, with variable rates across partitions (prset
ratepr=variable) and all other priors left at program defaults.

Two simultaneous independent analyses were run, each with four chains and
the default heating value, for a total of five million generations. The
consensus tree was generated using the sumt command in MrBayes with a burn-in
of one million generations, chosen post hoc after examination of
parameter convergence in Tracer. Chain mixing was adequate and all parameters
(including tree topology) converged rapidly. Equivalent analyses were
performed on the mitochondrial and the nuclear data alone to compare results
from single genome partitions.

Although the data partitioning and modeling scheme employed in this
analysis is probably overparameterized, Bayesian phylogenetic inference is
more robust to overparameterization than underparameterization
(Huelsenbeck and Rannala,
2004). In addition, the resulting topology was consistent with,
though not identical to, the topology obtained by a Bayesian reversible-jump
mixture model analysis of the same data set using BayesPhylogenies
(Pagel and Meade, 2004), which
employed two GTR + G models and no partitioning.

Experimental animals

We collected colonies of eight species of Odontomachus
representing a range of body sizes and ecologies
(Table 3), all of which were
also included in the phylogenetic analysis. Colonies were maintained in the
lab and fed a diet of mealworms, waxworms or crickets, three times per week.
All data were collected as described below with the exception of O.
bauri data, which were adopted from Patek et al.
(Patek et al., 2006) without
reanalysis and included with the other seven for comparison.

High-speed video and analysis

The protocol for filming of trap-jaw strikes was modified from Patek et al.
(Patek et al., 2006), using a
high-speed camera attached to a microscope (70 000–100 000 frames
s–1, 2–11 μs shutter speed; Ultima APX Photron, San
Diego, CA, USA; Leica MZ 12.5 stereomicroscope). Ants were fixed using a drop
of paraffin wax (applied to the top of the head) to the end of a rod that
could be rotated to keep the jaws perpendicular to the camera's axis. Animals
were hung by this translating rod in an empty beaker and stimulated to strike
by touching their `trigger hairs' with a thin metal probe of known diameter
(0.24 mm).

The kinematic data were used to calculate speed, acceleration and the lag
time (if any) between the first jaw to close and the second. Custom software
developed by the authors (available as Supplemental Items S1, S2 and S3 at
http://www.life.uiuc.edu/suarez/datasets.html)
in MATLAB (v. R2007a, Mathworks, Natick, MA, USA) was used to track the
mandible movements and calculate their angular and tangential speeds and
accelerations. An optimization technique was used whereby the root mean square
(RMS) error was minimized with reference to the coordinates of the center of
rotation and the size of each mandible. The mathematical challenge was to fit
a circle to a sequence of traced points; the circle would be the mandible tip
trajectory, and its center would be the center of rotation of the
movement.

The code was composed of two parts: the first traced the paths of the jaws,
and the second calculated speed and acceleration. Information from jaw-snap
films was input into the tracing module, including resolution (in dpi), size
(width and height in pixels), frame rate (frames s–1) and the
magnification factor of the microscope. Then, each frame in the sequence was
displayed as a MATLAB figure and the position of the mandible tips was
recorded in each frame. Also, the approximate position of the mandible base
was recorded for the first and last frames. These data were then stored as two
matrices of coordinates, one containing the mandible tip coordinates for each
frame and the other containing the mandible base location; the latter were
x and y coordinates averaged from the two sets. The data
were then saved and loaded into the calculations program.

The calculations program first built a grid of possible centers of rotation
about the averaged mandible base location. In addition, a column matrix was
constructed for each mandible that contained the possible values of each
radius for the traced circles. Using nested loops, iterations were performed
on the values of the centers of rotation and radii for each mandible and the
RMS error was calculated using the formula:
(1)
where T is the number of free parameters, xc and
yc are the coordinates of the center of rotation,
xi(t) and yi(t) are
the coordinates of the traced points at frame (t), S is
total number of frames tracked, and r is the radius of the best
fitting circle (Kreyszig,
1999). Once the centers of rotation and radii were found for each
mandible, the slopes of each were calculated throughout the sequence. From
these slopes, the angles were extracted. Angular velocities were then
calculated by multiplying the difference between slopes in radians with the
number of frames per second. The same procedure was applied to the difference
of angular velocities to obtain the angular accelerations. By using the dpi
and magnification data, the radii were expressed in units of meters, such
that, when multiplied by the angular velocities and accelerations, they would
yield their linear, tangential counterparts. Velocity and acceleration
profiles were plotted for each strike, as shown in Supplemental Item 1. The
Matlab-compatible scripts are downloadable from Supplemental Items 2 and 3,
and available from the authors upon request.

With accelerations derived from kinematic data (see above) and the mandible
masses (see below) we calculated peak instantaneous force using the convention
of Patek et al. (Patek et al.,
2006). The moment of inertia for a thin rod of length R
and mass M rotating around a fixed point
(I=1/3MR2) was used to calculate the force
(defined as the perpendicular strike force of the tip of the mandible atα–
max) as:
(2)
where M is the jaw mass, R is the distance from the center
of rotation to the jaw terminus, and α is the maximum angular
acceleration (in radians s–2).

Measurement error for digitization of strikes was estimating by retracking
and recalculating a representative two-jaw strike from each of the frame rates
used (70 000 frames s–1, 90 000 frames s–1,
and 100 000 frames s–1) five times, yielding a total of 12
single-jaw strikes for each re-tracked video segment. Percentage difference
from the mean was then averaged across all 12 strikes at each frame rate.

Filtering data

Differentiation of point-tracking data to produce velocity and acceleration
values has been considered problematic, particularly for acceleration data, as
it requires second order differentiation and is likely to amplify tracking
error (Walker, 1998).
Subsequent `choosing' of points of greatest acceleration, as we have done
here, might be expected to systematically overestimate mean maximum
acceleration values. We evaluated four combinations of methods for alternative
calculation of maximum velocity and maximum acceleration of a subset of the
data to determine whether our results could be improved by filtering. Both
cubic and quintic splines were fitted to the data, and tracking sequences were
differentiated using both two-point (the control, or baseline differentiation
method) and three-point differentiation methods, yielding six means (linear,
cubic and quintic spline fits, each with two differentiation methods). We
chose to use unfiltered, two-point differentiated data, as the spline-fit data
tended to slightly overestimate maxima, which did not solve our overestimation
problem, and the three-point differentiations resulted in unrealistically low
estimates (as much as 31% less) for acceleration, whether or not a spline
curve was fitted to the data points. Plots comparing effects of the filtering
techniques explored, can be seen in Supplemental Item 4.

We filmed four to six workers from each species and up to six strikes per
worker. Total strikes recorded and analyzed per species ranged from 13 (O.
chelifer) to 25 (O. cephalotes). Following jaw-snap recordings,
individual worker ants were killed by freezing and stored in a –20°C
freezer. To minimize changes in mass caused by drying, ants were stored in
air-tight vials and all mass measurements were made within 10 days of
freezing. We measured the following for each ant: whole-body mass, head length
(clypeus to apex), and head width [including the eyes; after Hölldobler
and Wilson (Hölldobler and Wilson,
1990)]. We then dissected out the mandibles of each ant and
measured them individually for mass and length. Linear measurements were made
using a Semprex Micro-DRO digital stage micrometer (0.005 mm resolution;
Semprex Corporation, San Diego, CA, USA) connected to a Leica MZ 12.5
stereomicroscope, and masses were measured using a UMX2 microbalance with 0.1μ
g resolution (Mettler-Toledo, Columbus, OH, USA).

Size measurements were log10 transformed, and TFSI [test for
serial independence, as specified by Abouheif
(Abouheif, 1999)] analyses were
performed using our phylogenetic hypothesis in the software PI v. 2.0
(Reeve and Abouheif, 2003) to
determine whether any of the following (log transformed) measurements showed
significant phylogenetic signal: head width, jaw length, body mass and jaw
mass. Similarly, values for speed, acceleration, raw and normalized force were
subject to the TFSI test to determine whether further statistical tests would
be influenced by statistical non-independence due to phylogeny; ANOVA and
post-hoc testing were only performed on species means that did not
show significant phylogenetic signal in the TFSI test.

For scaling relationships, head width was used as a proxy for body size, as
it is a standard measurement in the ant literature, and is a better predictor
of body mass across the subfamily Ponerinae
(Kaspari and Weiser, 1999)
than head length, which we verified for our test species with RMA regression
using RMA for Java (Bohonak and Van der
Linde, 2004; Sokal and Rohlf,
1981), as r2 for RMA regression of body mass
vs head width=0.99, whereas r2 for body mass
vs head length=0.98. Except where otherwise cited, statistics were
performed using Statistica software (version 6.0, StatSoft Inc., Tulsa, OK,
USA), and plots were produced using Excel 2003 (Microsoft Inc., Seattle, WA,
USA).

Because species values are not statistically independent, we used the
method of independent contrasts
(Felsenstein, 1985) as
implemented in the program PDAP in the Mesquite comparative analysis package
(Midford et al., 2005;
Maddison and Maddison, 2006)
to develop the scaling equations for jaw length, jaw mass and body mass, and
to produce the regression line for angular acceleration (alpha) and head
width. Continuous data for head width, jaw length, jaw mass, body mass, were
log10 transformed and input into PDAP along with the topology and
branch length data. With this information, PDAP provides hypothetical values
for ancestral nodes and normalizes them to produce contrast values. The
procedure of Garland et al. (Garland et
al., 1999) was implemented to produce scaling equations for size
parameters and to plot angular acceleration against head width. Linear
ordinary-least-squares regressions with the intercepts set to the origin were
performed on the normalized contrast values to calculate the slopes for the
scaling equations. Biologically meaningful intercepts for scaling equations
were calculated by substituting the mean values from the root nodes (which
serve as estimates of the ancestral conditions) for the independent and
dependent variable from each equation, the IC-corrected slope, and solving for
the intercept value. Contrast values and resulting slopes were checked using
independent contrasts derived in the Macintosh program CAIC
(Purvis and Rambaut,
1995).

Modeling force production using scaling equations

To predict values for maximum force perpendicular to the jaw surface across
a range of ant sizes based solely on scaling relationships, we parameterized
Eqn. 2 using the scaling
equations for jaw length and jaw mass (Eqn.
3a,
3b and Eqn.
4a,
4b, see Results section) and
angular acceleration, as functions of head width (Eqn.
6a,
6b). This curve was also
parameterized with scaling equations produced by phylogenetically uncorrected
OLS regression on the species means for comparison between force production
scalings that account for phylogeny, and those that do not.

RESULTS

Phylogeny

The phylogenetic hypothesis with relative branch lengths developed for all
exemplar species from combined data is shown in
Fig. 1. Odontomachus
is monophyletic in the combined tree, with Anochetus, another genus
of trap-jaw ants, as the most probable sister group. Nuclear-only and
mitochondrial-only trees (not shown) differed only in the rooting of the
Odontomachus clade and in the relative position of a single taxon
(O. ruginodis), but the single-gene trees were supported by posterior
probabilities 26% lower than our preferred, combined-data tree. Branch lengths
for internal nodes in the Odontomachus clade appear to be short
relative to those for terminal taxa in this group, and both topology and
branch-length information from the combined-data tree were included in the
subsequent comparative analyses.

Jaw usage patterns and temporal offsets

Five types of strike were seen: one jaw only (left or right), and two-jaw
strikes with the left jaw leading, right jaw leading, or simultaneous closure.
Leading jaw was defined as the jaw that achieved maximum acceleration toward
the midline first; closures were considered simultaneous when the two maxima
occurred in the same video frame. No significant pattern was seen within or
between species in terms of a preference for a leading jaw in two-jaw strikes
(34 were left-right, 38 were right-left; χ2=0.22,
P=0.64), whereas simultaneous closure occurred in seven of 79 two-jaw
strikes. Single-jaw strikes appeared to favor the left side (38 left-only
vs 18 right-only strikes, χ2=7.14, P=0.007).
All species examined included individuals that made both leading-right and
leading-left strikes, and despite low strike numbers per individual, 11 of 25
individuals exhibited both types of strike, and the remaining 14 were evenly
divided between `left-dominant' and `right-dominant' individuals.

Histogram of lag time between jaw firing in two-jaw strikes from all
species (N=79 strikes), mode=30–40 μs, mean=54 μs. First
bin represents simultaneous closure.

Most strikes were two-jaw closures with one jaw beginning to close one or
more frames after the first. The majority of two-jaw strikes (72 of 79 total
strikes) included temporal offset, but due to extremely rapid acceleration of
the second jaw, the second jaw often `caught up' with the first, and the two
jaws scissored past each other at or very near the midline of the ant's head.
However, the jaws closed simultaneously in the remaining seven strikes, or so
close to simultaneous that the tiny offset could not be resolved. Distribution
in lag time between maximum jaw accelerations for all strikes can be seen in
Fig. 2, with a mode of
30–40 μs. Distribution is unimodal with a long right-hand tail
representing strikes with long between-jaw lags, where one jaw closes
completely before the other begins to close.

Body size isometry

Across all species, the log–log regression slopes for independent
contrast values for jaw length, jaw mass and body mass against head width
(Fig. 3) did not allow
rejection of the null hypothesis of isometry. Jaw length (P=0.0053,
mean slope=1.12, 95% confidence interval for slope=0.61–1.63,
r2=0.75) scaled to the first power with body lengths,
whereas the slope of ∼3 for jaw mass (P=0.0018 man slope=3.26,
95% CI=2.07–4.45, r2=0.82) and body mass
(P<0.001, mean slope=2.94, 95% CI=2.03–3.85,
r2=0.87) indicated isometry between total body mass and
head width (Fig. 2), as mass
scales to the third power of linear size. The r2 values
were lower for jaw length than for length–mass plots (0.75 vs
0.82 and 0.87 for jaw mass and body mass, respectively), indicating that
across species, jaw length may be more variable than body mass and jaw mass as
a function of head width.

Scaling equations, expressed as functions of head width (h),
across independent contrasts are as follows, with Eqns
3a,
4a and
5a calculated using independent
contrast regressions, and Eqns
3b,
4b and
5b uncorrected:
(3a)(3b)(4a)(4b)(5a)(5b)
where R is jaw length, M is jaw mass and B is body
mass.

Mean maximum radial speeds for all jaws of eight species of
Odontomachus. One-way ANOVA significant (P<0.001).
Species arranged from left to right by mean mass (lowest to highest). Species
with the same letters (A–E) are statistically indistinguishable from
each other at the P<0.05 level in post-hoc pairwise
tests. Maximum jaw speeds of O. clarus desertorum and O.
erythrocephalus (group A) are significantly higher than previous highest
reported value for self-propelled prey strike in animals [O. bauri
(Patek et al., 2006)].

Speed and acceleration

Mean maximum radial jaw speeds differed significantly among species
(Fig. 4), ranging from
35.9±7.7 m s–1 in O. chelifer to
48.8±8.9 m s–1 in O. clarus desertorum,
bracketing previously reported values for O. bauri. The three
fastest-striking species (O. haematodus, O. clarus desertorum and
O. erythrocephalus) differed significantly from the three slowest
(O. ruginodis, O. cephalotes and O. chelifer), whereas
O. brunneus did not differ significantly from either of these groups.
Mean maximum jaw speed did not correlate significantly with head width or body
mass (P>0.05), and phylogenetic signal was not significant for jaw
speed using the TFSI test (P=0.21). Measurement error due to
digitizing for speeds and accelerations averaged ±6% and ±11%,
respectively.

Mean maximum angular accelerations varied from a value of
1.31×109 radians s–2 in the smallest species
(O. ruginodis) to 3.87×108 radians
s–2 in the largest (O. chelifer;
Fig. 5A). With the TFSI test
indicating that angular acceleration values showed significant phylogenetic
non-independence (P=0.02), independent contrast values were
calculated prior to further analysis. Regression of independent contrasts (IC
values) of angular acceleration on head width ICs
(Fig. 5B) yielded the following
equation:
(6a)
(95% confidence interval for the scaling coefficient of –3.03 to–
0.05) and the phylogenetically uncorrected species values yielded the
following equation:
(6b)
(95% confidence interval of slope –3.44 to –0.58), where α
is the angular acceleration in radians and h is the head width.
Neither slope differs significantly from the null expectation of –2 that
would be assumed if muscle cross sectional area scales isometrically.

Re-running the TSFI analysis following calculation of independent contrast
results showed that phylogenetic signal was no longer significant when
independent contrast values for acceleration were used (P=0.27).

Predicting jaw performance based on size parameters

Predicting force production based on a single scaling parameter (head
width) yielded a curve showing maximum single-jaw force production increasing
a range of head widths. This was done by parameterizing
Eqn. 2 by substituting Eqns
3a,
4a and
6a for M, R and α.
Plotting model predictions for a range of head widths yielded the curve shown
in Fig. 6B, with maximum jaw
force continually increasing as a function of head width.

General predictions from modeling force production based on scaling
equations (both phylogenetically corrected and uncorrected) were then compared
to the forces estimated from the original species data
(Fig. 7). Comparing species'
measurement-based maximum force values with general size-based model
predictions (as in Fig. 6B)
showed a mean absolute difference of 12% when phylogeny was accounted for, and
11% when compared to the phylogenetically uncorrected model
(Fig. 7). Size-based force
predictions from phylogenetically corrected scalings differed from those made
with uncorrected (or `star phylogeny') scalings by an average of 3%.

DISCUSSION

The kinematic data presented here show a large range of jaw
force-generation abilities in the genus Odontomachus: a nearly
fourfold difference between the largest and smallest species, scaling with a
related range of sizes but varying considerably (±12%) from strictly
size-based expectations. In the context of the phylogeny, this variation gives
us clues to which features may be most evolutionarily labile, giving rise to
relatively high- and low-force producing species. Comparing phylogenetically
corrected and star-phylogeny models suggests that differences in performance
relative to the model may be due to relatively recent selection pressures.

Jaw-lag and jump performance

As in previous work on O. bauri
(Gronenberg and Tautz, 1994;
Patek et al., 2006), both
mandibles rarely snapped shut synchronously. The lag between jaws followed the
same general pattern previously demonstrated by Patek et al.
(Patek et al., 2006), where
lag time between individual pairs averaged ∼40 μs; however, the
synchronous closing in a small number of snaps (seven total strikes, in three
species – O. haematodus, O. clarus desertorum and O.
cephalotes) suggests the time-lag does not represent a minimum time for
neural conduction from one mandible to the other. It is possible that the `no
lag' strikes are triggered differently from the strikes exhibiting the lag,
perhaps by having both jaws stimulated simultaneously, assuming that most
strikes result from a stimulation of the trigger-hairs on one side of the
cocked mandibles and require conduction to the other jaw for firing of both
jaws.

Alternately, there may be an adaptive explanation for a lag between
mandibles if temporally off-set strikes either help prevent damage to the jaws
if the target is missed or create greater force at impact with the second
mandible as the target gets displaced towards the midline by the first. Jaw
lag might also be expected to contribute to the jump trajectories of the ants,
possibly introducing a rotation about the ants' head-to-vent axis, or tending
to throw the animal sideways rather than vertically. However, without a model
that translates jaw speed and acceleration into jump performance, and video
data from jump sequences that can resolve distances, angles and speeds of
individual jaws as they contact substrates during the acceleration phase of
jumps, this hypothesis cannot be tested. The lack of such a model also limits
our ability to make predictions about jump performance with the current
dataset, as existing models for jumping are based on acceleration during
extension of jointed legs (e.g. Alexander,
1995) rather than rapid rotation of opposing fixed-end jaws
against a substrate.

Phylogeny, head size and force production in Odontomachus. Head
sizes are species means, scaled to 2 mm bar. Bar graph shows force production
predicted by independent-contrast model (blue bars), species mean data (maroon
bars), and star-phylogeny model (beige bars) for each species studied. Forces
calculated from actual species means differed from head width-based
predictions from phylogenetically corrected models by an absolute mean value
of 12%, and from the uncorrected models by 11%. Predictions derived from
uncorrected (star-phylogeny) and phylogeny-corrected models differed by an
average of 3%.

Scaling and force-production in trap-jaw ants

Morphological variation across the eight species of Odontomachus
examined here showed the simplest pattern of differentiation
(Wheeler, 1991;
Wilson, 1953), where worker
variation follows a continuous, linear isometric or allometric curve. Without
a larger sampling regime, it is impossible to reject among-species variation
along slopes that conform to the simplest submodel of continuous linear
variation, that of isometry. This contrasts with the allometric, clearly
differentiated morphological castes
(Wilson, 1976), found in some
species of polymorphic ants.

Under any scaling model, maximum force, as a product of jaw mass, jaw
length and angular acceleration, would be tightly linked to mandible mass and
length. As seen here, in even the slowest-accelerating Odontomachus
examined (O. chelifer), large values for mass and length compensated
for reduced acceleration, resulting in a fourfold greater force generation
than seen in the smallest species (O. ruginodis), despite the latter
having the highest mean maximum angular acceleration of the species studied.
Species mean values generally track model predictions well, with variation
from model predictions falling within standard deviations for all eight
species. Despite the positive relationship between maximum force and size,
there appears to be no clustering of species at the high end of the range of
sizes seen, nor is there any obvious trend toward larger size in more derived
species in the phylogeny.

It is worth noting that when not performing full lock-and-release
strikes, Odontomachus ants have been shown to have some of the
slowest jaw movements of any ants, as their adductor muscles, though quite
large, are composed almost entirely of long-sarcomere, slow-contracting fibers
(Gronenberg et al., 1997).
Most ants have a mixture of long- and short-sarcomere fibers in their jaw
adductors, and their jaw movements may be five to ten times faster than
non-power-amplified Odontomachus jaw closures
(Gronenberg et al., 1997;
Paul and Gronenberg, 2002).
The low speeds of normal jaw movements do not appear to be a problem for these
ants, as the workers are generally monomorphic and can perform all nest tasks
(carrying food, moving larvae and eggs, moving nesting materials) using their
oversized, slow-contracting jaws.

Of the species studied, O. chelifer is the clear champion in terms
of force production (Fig. 6A).
Laboratory observations (A.V.S. and J.C.S., unpublished data) show that these
robust ants do indeed deliver devastating strikes, such that they seldom, if
ever, use their stings in attacks on prey animals – a single strike is
usually enough to disable the prey item. This is in contrast to smaller
species, which generally strike and subsequently sting to disable prey.

With continuous, log-linear size variation and multiple species with
workers considerably smaller than the largest Odontomachus species,
it appears that optimal size for a particular species is not dependent on
maximum force production. More likely, in such an isometric context, maximum
size is balanced against the developmental and physiological costs of growing
and carrying (and loading) oversized adductor muscles and jaws. Alternative
hypotheses need to be examined including those relating to `optimal speeds'
for capturing elusive prey such as springtails
(Brown and Wilson, 1959), or
`ecological release' relative to jaw performance – wherein there is no
natural enemy or prey item requiring such extreme speed or force production,
so that individual size is determined by other selective pressures, such as
food availability or optimal size relative to available nesting sites. In
other ant lineages where trap-jaw morphologies have evolved independently,
including taxa in the Myrmicinae
(Gronenberg, 1996b) and
Formicinae (Moffett, 1985)
subfamilies, we might expect to see similar species-scaled differences in
performance, although isometric scaling cannot be assumed for these.

Although the workers of most Odontomachus species show little
variation in size within a single colony, some species do have workers within
a colony that exhibit a range of sizes (e.g. O. cephalotes, a
Northern Australian species). Detailed study of species with broad
intra-specific distribution of worker sizes, including characterization of
behavior of individuals by size and age, will help determine how trap-jaw
phenotypes are tuned by the social environment, development and evolutionary
history. More generally, greater within-species sampling and narrowly focused
study of species that may deviate from the log-linear relations presented here
will be valuable in understanding the selective pressures contributing to
diversity (Biewener, 2003) in
trap-jaw ants.

The predictions of this paper should also be tested via direct
measurements of force production across these (and other)
Odontomachus species. The behavioral ecology, including prey and
natural enemy types, and relative frequency and ecological correlates of jaw
usage (jumps vs strikes) remains largely unknown, and may help
explain the preponderance of relatively small species.

Phylogenetic comparative methods

The Odontomachus phylogeny developed here, with its relatively
short internal branches, suggests the possibility that this genus diversified
quickly, with fewer subsequent speciation events following an original
radiation, or an increase in extinction rate leaving relatively long terminal
branches. Alternatively, our sampling regime may have been broad enough and
evenly distributed enough to create relatively long branches as an artifact.
In either case, it approximates the `star phylogeny' assumed in use of
non-phylogenetically corrected species data, and is less likely to be
confounded by an uneven distribution of recently and less-recently diverged
species (Garland et al., 1999;
Price, 1997). Despite this,
the results of the TFSI tests demonstrated significant phylogenetic signal in
key parameters expected to influence force production, particularly jaw
acceleration, arguing for incorporation of statistical methods correcting for
phylogeny.

We found only small differences between jaw-strike forces predicted by the
phylogenetically corrected and uncorrected models for force production.
However, there is still significant value added when the data are viewed in
the context of the phylogeny, both from first principles and in terms of the
quality of results for purposes of additional hypothesis generation and
testing. First, without a phylogeny, there is no a priori way to know
what the effect of accounting for branching patterns and branch lengths would
be, and the assumption that it will not influence the outcome has been shown
to be incorrect in numerous studies (e.g.
Nunn and Barton, 2000;
Zani, 2000;
Smith and Cheverud, 2004).
Second, given that the data appear to contain phylogenetic signal according to
the TFSI tests, but that accounting for that signal does not necessarily
improve predictions of force-generation performance for the actual terminal
taxa, we can make inferences about evolution of the trap-jaw system that would
otherwise be difficult to support. In the present study, the situation where
phylogenetic signal may exist but does not account for the differences in
performance between taxa may be a case like that presented by Price
(Price, 1997) where a variable
character has been under recent selection in the individual species'
environments, and the contrast data, representing relatively deep divergences,
can be overwhelmed by recent adjustments in the character – in this
case, body size, with performance scaling in simple isometry with changes in
size.

ACKNOWLEDGEMENTS

The authors thank Brian Fisher of the California Academy of Sciences, Chris
Smith of University of Illinois and Mark Deyrup of the Archbold Field Station
for assistance in collecting and maintaining ant colonies, and Joe Baio and
Tawny Mata for assistance with filming strikes and data processing. We also
thank the following individuals for loan of specimens for phylogenetic
analyses: Lloyd Davis, David Donoso, Kim Franklin, Jurgen Liebig, David
Maddison, John Mangold, Wendy Moore, Maruyama Munetoshi, Chris Smith and Alex
Wild. For permission to collect and import ants, we thank the Ministry of
Environment and Energy (Permit 122-2004-OFAU) of Costa Rica, the Ministerio de
Salud y Ambiente (Permit 20202/05) of Argentina, the Administracion de Parques
Nacionales (Permit 002870-2) of Argentina, James Cook University, Australia
for the loan of O. cephalotes specimens and the United States
Department of Agriculture (APHIS import permit 69963). This work was supported
by a seed grant from the Beckman Institute for Advanced Science and
Technology.

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